Question

if sin theta=4/5 what is tan theta

Answer 1

Step-by-step explanation:

$\huge\underline{Answer-}$

$\sin\theta = \frac{Perpendicular}{Hypotenuse} \\ \\ \bold{Given - } \\ \\ \sin\theta = \frac{4}{5} \\ \\ \underline{ It \: means,} \\ \\ \fbox\bold{Perpendicular = 4} \\ \\ And \\ \\ \fbox\bold{Hypotenuse = 5} \\ \\ \bold{We \: need \: to \: find \: Base} \\ \\ (AC) {}^{2} = (AB) {}^{2} + (BC) {}^{2} \\ \\ (BC) {}^{2} = (AC) {}^{2} - (AB) {}^{2} \\ \\ BC = \sqrt{(5) {}^{2} - (4) {}^{2} } \\ \\ BC = \sqrt{25 - 16} \\ \\ BC = \sqrt{9} \\ \\ \fbox\bold {BC = 3}$

$\bold{To \: Find - } \\ \\ \tan \theta = \: ? \\ \\ \fbox\bold{\tan \theta = \frac{Perpendicuar}{Base} } \\ \\ \fbox\bold{\tan \theta = \frac{4}{3} }$

NOTE -

Triangle ABC is a Right-angle Triangle

Answer 2

Answer:

4/3

Step-by-step explanation:

Given:

sin∅ = 4/5

To find:

tan∅

Solution:

We know that,

sin∅ = Perpendicular(p) / Hypotenuse(h)

Therefore, Base(b) = √(h²-p²)

= √(5²-4²)

= √(25-16)

= √9

= 3

Now, tan∅ = p/b

or, tan∅ = 4/3

The required value of tan∅ is 4/3 .